% % lsThe "( directory listing ) % cp file1 file2 ( copy file1 to make file2 ) % logout ( logs you off the computer )
tar xvzf nc.tgz
This creates the folder "nc" and several subfolders.
Go into the nc folder and run "make":
cd nc
make
This makes the simulator and several other useful programs.
You must place them into a folder, such as ~/bin, your personal
binary folder, or other bin folders that you have in your
shell's path:
cd bin
cp nc stim plotmod vid ~/bin
or e.g:
su root
cp nc stim plotmod vid neurc /usr/bin
Or else add the "nc/bin" folder to your path:
vi ~/.cshrc
add "~/nc/bin" to the path
Note that there are some useful programs in "nc/bin":
bins.c makes histogram
column cuts 1 column from an output file.r
ncd runs nc to display morphology ("nc -d 1")
ndv runs nc to display morphology ("nc -d 1")
ncv runs nc with vid
ncplot displays file.r on vid ("plotmod $argv | xvid")
replace replaces string in files ("replace str1 str2 files")
xvid makes a larger window than vid
etc.
For example, from the command-line prompt: % kate circuit1Or, you can rely on a GUI editor like "soffice", or "openoffice". Run the editor by clicking on its icon, then click on "File" and then "New" to make a new file.
There are two modes, visual mode and command mode.
In visual mode (where you initally get to) typing "i"
gets you into insert mode. Any keys you
type at this point will go into the file. To get out
of insert mode, hit the
After you type in your NeuronC program, you run the
program by typing one of the following commands:
NeuronC is a language and simulator program for
simulating complete physiology experiments on neural
circuits. With the NeuronC language, you can describe
and simulate a neural circuit as well as a complete
stimulus and recording paradigm. Stimuli in NeuronC
can be voltage or current clamps at single locations in
the neural circuit or may be 2-dimensional patterns of
light which cause simulated photoreceptors to transduce
visual signals. Thus, NeuronC is especially designed
for simulating visual neural circuits.
NeuronC has 2 distinct modes of operation,
"construction" and "run". In the "construction" mode,
NeuronC builds a neural circuit from programmed
instructions, along with stimuli and recordings.
In the "construction" mode, you can perform simple
calculations, program loops, procedures and subroutines
to define neural elements. You may organize these
procedures to create a neuron or circuits of many
neurons. You may also include stimuli and records in
loops and procedures. "Construction" mode is familiar
to computer programmers because it is similar to a
language like "C" in which procedures are used to
accomplish tasks.
NeuronC has several types of neural elements. These
connect to either 1 or 2 nodes, and the nodes must be
given when the element is defined. The types are:
To build a neural circuit, you need to include at
least one neural element statement and some stimulus
and plot or print statements:
A neuron receives signals through synaptic
connections from other neurons. The synapse evokes a
post-synaptic potential (PSP) by opening or closing
channels in the post-synaptic membrane.
Construct a presynaptic terminal, a synapse,
and a segment of a neural dendrite. Stimulate the
presynaptic terminal with a voltage clamp, and record
the post-synaptic potential. Use the editor to make a
file (or use existing "mod1.n"):
Next, run the program "mod1.n" by typing:
NeuronC runs a voltage-clamp stimulus to open
synaptic channels at 5 msec, and closes the channels 10
msec later. NeuronC plots a graph showing voltage and
current vs. time on the screen. Each "plot" statement
makes a different color line on the graph.
1) The green line represents the presynaptic
potential, or -45 mv in this model. After the voltage
clamp is turned off at 15 msec, the green line decays
to resting potential (-70 mV).
2) The synapse is depolarizing. The blue line
represents the time-course of the post-synaptic
potential (PSP), which peaks at about 20 mV above
resting potential.
3) The post-synaptic membrane potential does not
reach the synaptic reversal potential (0 mv) because
the membrane conductance (1/resistance) shunts current
from the synaptic conductance. The post-synaptic cable
segment is quite long and has a large surface area, so
its membrane conductance is relatively high.
4) The voltage decay of the post-synaptic membrane
reflects membrane properties (tau), as well as synaptic
properties (default synaptic delay dfta = dftb = 0.2 msec).
5) It may be helpful and fun to try changing some
of the parameters. What happens if you change synaptic
"thresh", or the "vclamp" value?
Background: Neurons in the retina have special shapes
(morphology) tuned for their function. The morphology
of some neurons imparts a "weighting function" to
synaptic inputs that originates in "electrotonic
decay".
A long neural dendrite approximates an infinite
cable which causes a voltage at one point to decay
exponentially along the dendrite. An important
parameter for a neural cable is lambda, or "length
constant", which is the distance along the cable that
is required for the voltage to decay to 1/e or 37%.
Problem: How far along a dendrite must a neural signal
travel for its voltage to decay to 37% (1/e)?
Model 2: Construct a cable long enough to observe
exponential decay and stimulate it by injecting current
with the synapse created in "mod1" at one end. Record
voltages in the cable at various locations. Use the
editor to make a file containing the following
lines (or use "mod2t.n"):
% vi mod2t
Notes for mod2:
1) Verify that the time constant (time to fall to 63% of
maximum voltage) of the presynaptic node is about 5 msec.
This can be calculated as Rm= 5000 Ohm-cm2 * Cm = uF/cm2.
2) Verify that the voltage on the red line (node 4),
after it reaches an equilibrium value at 10 msec is
near 37% of maximum on the blue line (node 1).
Thus, lambda is about 360 microns (3 * 120) for the
cable.
3) Note that the stimulus takes a few msec. to reach
the distal end of the cable. The conduction velocity
may be calculated as:
1) Remember that the signal is measured by
subtracting the resting potential (-70 mV) from the
voltage measured in the cable. Verify from the plot
that lambda (37% of the maximum signal) is about 350
microns. In this model, Rm=5000 ohm-cm2, Ri=100 Ohm-
cm, so lambda is calculated to be 354 microns for a 1
micron diameter cable.
3) Since the cable is not infinite, its decay is
not exactly a simple exponential. Verify that the
voltage decay in "mod2s" is not exponential near the
distal end (nodes 4-6). At the distal end (away from the
synapse), no current leaks through the end of the
cable. Therefore the voltage does not decay there, and
the voltage vs. distance plot approaches a level slope.
1) Note that the post-synaptic potential is larger.
This is because the cable's resistance (both rm
and ri) is higher with a smaller diameter. Now the
voltage at node 1 approaches the reversal potential for
the synapse (near 0 mV).
2) Verify that decreasing diameter by a factor of 10
decreases lambda by a factor of about 3 (square root of
10). Lambda (distance for decay to 37% of max) is now
about 100 microns.
3) Verify that the voltage decay is exponential
between segments (voltage decreases by roughly a
constant factor at each segment) for the smaller 0.1
micron diameter cable. Voltage decay is more
exponential because the cable is several "lambdas"
long, so the distal end does not affect the proximal
end much.
Next, change "drm" (default Rm) from 5000 to 50000
and observe the corresponding changes. Note that this
increases lambda to near 350 um, but has little effect
on the PSP amplitude. This is because the synaptic
output is already near its "driving" potential, and the
post-synaptic potential is said to be "saturated".
Note: A change in either Rm or diameter causes an
equivalent change in lambda.
Problem: How does a spine affect a synaptic input signal?
Model 3: Construct a shorter cable than in the previous
model, and attach spines at the 2 ends. Use the editor
to create a new file (or use existing "mod3.n"):
Notes for mod3:
1) Verify that the voltage difference across the
length of spine 1 (the red line) is about 20 mV, and
that the decay along the larger dendrite (the green
line) is about 5 mV.
2) The axial resistance "ri" in the spine neck is
much greater than the axial resistance in the main
dendrite. Therfore, most of the voltage drop occurs in
the spine neck.
3) To understand this reasoning, imagine injecting
water into a leaky garden hose with a hypodermic
needle.
4) The value of the axial resistance "ri" is more
affected by reduced cable diameter than rm, because ri
is inversely proportional to the square of diameter:
5) The output spine (spine 2 in "mod3", the blue
line) does not cause a large voltage drop. This is
because its resistance is high and therefore only a
small current enters it. Thus, the voltage drop across
ri is also small. Imagine the minor loss of pressure
when filling a hypodermic needle with a garden hose.
The effect of a synaptic input on a neuron's signal
can vary markedly, depending on the location of the
cell's input and output. A synapse has a relatively
high resistance compared with the total resistance of
the neuron. If Rin (input resistance of the neuron)
seen by the input synapse is high, the synapse drives
the postsynaptic membrane easily but the membrane
voltage may saturate, causing a non-linear signal
transformation. However, if Rin seen by an input
synapse is low, the synapse cannot drive its post-
synaptic membrane well. For this reason, the electric
signal from a single synapse within a neuron does not
transfer well from dendrites to the low-resistance
soma, because the low resistance shunts the signal.
If a neuron's output is derived from this low
resistance soma (e.g. as in a ganglion cell), then the
output signal collected from an individual synaptic
input is reduced by this low resistance. However, the
electric signal collected by the soma from many input
synapses does reflect the average synaptic input (e.g.
ganglion cell, horizontal cell). This average signal
transfers well to distal dendrites, if they are thick
and have low axial resistance (e.g. horizontal cell),
because dendrites usually have a higher input
resistance than the soma.
If an output synapse is located in a tapered distal
dendrite with relatively low axial resistance (e.g.
horizontal cell), the soma's signal can effectively
drive the output synapse. If, however, the output
synapse is located near input synapses in a fine distal
dendrite with high axial resistance (e.g. wide-field
amacrine cells), its signal may reflect nearby input
synapses rather than the soma's signal.
Thus, the effectiveness of synaptic transfer from input
to output reflects both dendritic morphology and
relative position of the synaptic inputs and outputs.
Problem: How does anatomy and membrane biophysics of
horizontal cell affect voltage response at different
parts of cell?
Model 4) Add a soma to model 3 and test the effect of
varying soma location with respect to the input and
output spines. Copy the previous modeling file
("mod3.n") to make another file:
1) Verify that the soma increases voltage drop
along spine 1 (red line) and the main dendrite, but
does not affect voltage drop in spine 2 (blue line).
2) Verify that voltage decay is now greater than
exponential, that is, voltage decay is now relatively
linear in each segment, not constant in ratio.
Move soma to proximal location:
Next, copy "mod4" and make a new version "mod4a" in
which the soma is located at the branchpoint for the
input spine (node 1). This time, run the 2 versions
together so you can compare them:
Note that the effect of locating the soma directly at
the input spine is to increase voltage drop across the
spine neck. However, now there is a slightly larger
signal at the soma, because the signal is not reduced
by voltage drop due to the axial resistance (ri) along
the main dendrite. But for the signal at spine 2, the
soma location doesn't matter much.
Move soma halfway:
Make another version of "mod4", say "mod4b". Modify
"mod4b" to locate the soma halfway between spine 1 and
spine 2 (node 3), and run the model again. Run the 3
versions of mod4 together:
The effect of additional horizontal cell branches on
the signal from one synapse can be simulated by
the soma. The soma's effect is to shunt electric
current and therefore to increase voltage drop along
the axial resistance of the dendrites and spines.
To see a display of the neuron in mod4.n, you can add
display statements. However to correctly display the
neuron, all of its nodes must be given locations with the
"loc" parameter. The mod4d.n model is the same as mod4.n
but has the node locations defined and includes the display
statements. Run mod4d.n like this:
Problem: What is the effect of electrical coupling in a
small array of cones on the signal from one cone?
Model 5) Create a small array of cones (modeled here as
single compartments) and couple them into a 2-
dimensional array with gap junctions. Also create an
isolated cone for comparison. Stimulate the array with
a small spot over the central cone, and record the
responses of a line of cones. With the editor, create
a new file (or use existing "mod5t.n"):
2) Note that the response of cones near the edge
of the array is lower in amplitude and delayed in time,
compared with the central cone's response.
Next, modify "mod5t.n" for a spatial plot. Copy mod5t.n
into a new file "mod5s.n" and modify it to look like
this:
(mod5s should look like this:)
By recording from a line of cones, "mod5s" gives a
spatial plot similar to a receptive field map of a
single cone. Note that the spatial response of the
cone array looks somewhat exponential (actually a
modified Bessel function). The space constant for the
array's response is approximately 2 cones or 10 um
distance.
The space constant can be varied by changing the
gap junction conductance. Try increasing and
decreasing the conductance by factors of 2, and then
try increasing by a factor of 1000 to simulate closed
gap junctions.
In real experiments, a stimulus always has some
optical blur. To see the effect of optical blur,
try increasing the size of the stimulus light spot to
15 microns in diameter. This causes a larger response
by stimulating several cone photoreceptors, and changes
the shape of the cone receptive field.
To see the effect of totally isolating the cones, you
can try copying "mod5t" to make "mod5ti", and add the
following lines to "mod5ti":
Problem: What is the space constant of a fine
dendritic process that contains varicosities and
synaptic inputs?
Model: Construct a fine (0.1 um diameter) dendritic
cable with varicosities (4 um diameter) spaced every 10
um. Locate a synaptic input at one varicosity.
Stimulate the synapse, and record voltage in the local
varicosity as well as in other distal varicosities.
With the editor, create a new file ("mod6t.n"):
This model consists of 10 varicosities and fine
cable segments connected as beads on a string,
connected on one end to a small soma. A synapse is
located at varicosity 5, which is near the center of
the cable. Verify that the voltage at this node is
greater than other nodes, and that it reaches an
equilibrium potential near 10 msec, when the stimulus
gets turned off.
Now, try the space plot. Make another file "mod6s"
by copying "mod6t". Erase the "plot" lines and put in
the "graph" lines:
1) Note that the dynamic range of the signal is
about 55 mV. This results because the synapse is
turned completely on and then off.
2) Verify that lambda is about 3 cable segments long
(30 microns). The green graph lines represent the
voltage along the dendrite during rising stimulus, and
the red lines represent the falling stimulus. This is
longer than lambda for a 0.1 micron dendrite (see Model
2) which is near 100 microns. The effect of the
varicosities is to act as "radiators" for the electric
current. The effect of the varicosities is to decrease
membrane resistance for the fine dendrite.
To investigate the effect of synaptic conductance at
all the varicosities, locate synaptic inputs at all
varicosities. This time, stimulate the original
synapse as before, but stimulate the others as well.
Construct additional extra synapses by removing the
comments around the second "stim" statment in "mod6s".
Also remove the semicolon at the end of the first stim
statement. The two stim statments should look like
this:
1) The extra synapses are activated throughout the
duration of the model and therefore do not directly add
to the signal. However, the effect of the extra
synapses is much like a varicosity: an activated
synapse can reduce membrane resistance and therefore
passively reduce signal spread.
2) Verify that the dynamic range (from activated on
to inactivated) of the signal is only about 8 mV now.
This occurs because the decreased membrane resistance
shunts electric current laterally.
3) Note that after the stimulus is turned off, the
red line shows an "inverted V" which is the result of
turning off the signal synapse at varicosity 5 while
the other synapses remain activated.
4) Verify that lambda is now about 10 microns. This
much reduced lambda implies that under certain
conditions a) synaptic connections can control lambda
in fine dendritic trees, and b) the signal in each
varicosity can be effectively controlled by its input
synapse, irrespective of signals in neighboring
varicosities.
The scomp models look very simple. They consist of just one
compartment with several membrane channels, and they generate
spikes according to the current injected into the compartment.
However, the simplicity of the model can be misleading at first.
When more than 1 or 2 membrane channel types are included in a
compartment, the complexity factor rises exponentially, so that
it can be very difficult to predict with intuition what will
happen, or even to understand the role of each channel.
The first scomp model is "nc/tcomp/scomp_fm.n". This model is a
close match to the model presented in Fohlmeister & Miller
(1997a), in which a single compartment model of a spike generater
from salamander ganglion cells is described.
Next, the single compartment cell is defined:
Next, the channels are added to the soma, each with its type
specified, its density (in S/cm2), possibly with noise properties
(chnoise), and a name for the channel so it can be plotted as a
trace on the output graph.
The "onplot.m" file contains functions to run at plot time. The
"onplot()" procedure in "onplot.m" runs at the plot interval but
runs before any of the other plots are generated. In this case,
it calls the spikplot() procedure which calculates the
instantaneous spike frequency from the spike interval, and it
also calls the calc_totcur() function in the scomp_fm.n model,
which calculates the total channel current in the model.
Next the experiments are defined. Each one is called when its
name is found in the "expt" parameter, set by default to "spike".
You can change the experiment that runs by changing the value of
"expt" on the command line:
neurc --expt spike scomp_fm.n
or
neurc --expt isi scomp_fm.n
or
neurc --expt f/i scomp_fm.n
The "scomp_fm.n" model file contains several experiments that are
run on the same spike generator. The "spike" experiment is run by
default. It generates 1 spike, showing the currents during the
spike:
Several of the plots show the separate currents from each channel
type. There is also a plot of the compartment voltate showing the
spike, and there is also a plot of the total current from all the
channels (the dark red trace). The skca5 and bkca channels are
disabled by default, but you can enable them by uncommenting
them.
The lesson in the model is to try to understand the role of each
current in generating the fast-rising and fast-falling spike.
The model starts out with a 250 pA current to activate the Na current,
ant at 0.5 msec the current is reduced to 150 pA. From there, the
Na current slowly builds up until about 2 msec, after which it
rapidly becomes regenerative. This meas that when the Na current
activates, it depolarizes the cell which causes it to be more
activated. This effect is known as "positive feedback" in control
systems theory, and is responsible for the very fast rise of the
spike's leading edge.
After the spike has depolarized to its peak, the Na current
inactivates. This allows the spike to repolarize (hyperpolarize)
but it would not do this very fast unless K currents are present.
So at the same time, the Kdr ("delayed rectifier") current gets
activated by the depolarization of the spike, and starts to
hyperpolarize the cell, once the Na current has decreased by
inactivation. There is another effect on the Na current -- it
decreases just when the spike is most depolarized because the
driving force (Vna - Vm) for the Na current is less.
Once the Kdr current turns on, the spike repolarizes in a msec or
so -- and it actually hyperpolarizes below the original voltage.
This hyperpolarization deactivates the Kdr channel -- it does not
inactivate automatically as the Na channel does, but deactivates
when the depolarization that originally activated it is not
present. In addition, the KA channel is activated by the leading
edge of the spike. It, however, inactivates like the Na channel
soon after it is activated. Together the Kdr and KA currents
terminate the spike. During their activation, and immediately
following it, there is said to be a "refractory period" during
which it is not possible to generate another spike, even with
a large injected current. One function of the refractory period
is to allow all the voltage-gated channels to recover from their
activation during the spike, to allow another spike to occur with
the same waveshape as the first one.
In this scomp_fm.n spike generator, the role of KA appears to be
more important in terminating the spike than in regulating the
inter-spike interval. The reason is that other channels take the
role of regulating the inter-spike interval. The Ca channel is a
little slower than the Na channel, and but it turns on during
each spike and allows some calcium to flow into the cell. This
calcium is then a signal for how many and how fast the spikes
occur. There is also a calcium pump that removes calcium from the
cell and pumps it to extracellular space. The SK and BK Ca
channels sense the calcium and hyperpolarize the cell when the
calcium level goes up. The BK channel (commented out by default)
is sensitive to both Vm (membrane voltage) and [Ca]i (the
internal calcium level), so it is activated only during a spike
when [Ca]i is high. It is very fast, which allows it to shorten
the spike duration when the [Ca]i is too high, which will then
reduce the amount of calcium that flows into the cell. BK
channels are often involved in generating a strong
after-hyperpolarization, but like Kdr they are also deactivated
by hyperpolarization so they soon turn off after a few msec.
The SK channels are activated only by internal calcium [Ca]i, not
by voltage, so they act only on the accumlulated calcium in the
cell. This makes their role very straightforward -- they
hyperpolarize the cell after a burst of spikes when the [Ca]i
gets high. This allows the cell to have spike frequency
adaptation. While there are several other mechanisms that can
accomplish spike frequency adaptation, such as slow inactivation
of the Na channels (sometimes by delayed recovery from
inactivation), the SK channels are a well-known regulator of
spike frequency. The SKCa1 channel is much slower than Kdr, and
has a time constant of ~50 msec, and the SKCa2 channel is even
slower with a time constant of ~400-500 msec. This gives them
full control over very long inter-spike intervals.
To run the "isi" experment, enter:
In this "isi" (inter-spike interval) experiment, the emphasis is
on what happens between the spikes. During the first spike,
calcium in the cell [Ca]i rises, and then slowly drops due to
being pumped out of the cell. But this calcium activates the
SKCa1 channel, which can then regulate the ramping up
depoarization to the next spike.
Note that the largest current in the beginning of the inter-spike
interval is the SKCa1 current. This means that it is the current
that controls the overall spike rate (given a specific injected stimulus
current), not the Na or KDR, KA channels. Typically in the axon
of a neuron, there are only Na and Kdr channels, which take on
the role of transmitting spikes quickly along the length of the
axon. In the axon the Na and Kdr channels have overlapping
voltage activations, i.e. both currents are typically activated
at rest. This prevents any small currents from affecting when the
next spike will occur -- a spike can only occur if a spike
traveling along the axon depolarizes the Na channels in the
presence of the continuous Kdr channel activation.
However, in a spike generator, it is important that the Na and
Kdr, KA currents are small, essentially off, at the resting
membrane potential, i.e. that other currents control the resting
membrane potential so they can regulate the inter-spike interval
and thus the overall spike rate. The BK and SK channel currents
can control spike rate because they are larger than the Na, KDR,
KA currents. But the BK and SK currents are small. They have to
be, to allow the synaptic input to the cell to be the main
control for the spike rate. This is the main function of a spike
generator -- to generate spikes according to very small
depolarizations (EPSPs) from synaptic currents.
If you uncomment the "skca2" and "bkca" channels, they add to the
hyperpolarizing influence in the cell and increase the
inter-spike interval. This makes the plot of all the currents a
little more complex, and to see the next few spikes, you need to
uncomment the second "endexp = 0.5" statement. This shows what
happens in a typicalburst of spikes. The first spike lets in
some calcium, but not enough to activate the BK and SK channels
much. But after the second spike, the BK channels turn on at a
more hyperpolarized voltage, and the SKCa1 chanel gets activated,
which slow down the ramping up depolarization after the intial
after-hyperpolarization. The spike rate eventually slows to a
plateau frequency that is set by the BK and SK currents in
response to the spikes generated by the injected current.
If you then replace the comments around the bk and skca2 channel
definintions, and run "expt f/i", you can see the spike rate
at different currents. The little circles show the instantaneous
spike rate from one spike to the next. If you then uncomment bk
and skca2 and change their density with the "skca1_mult",
"skca2_mult", and "bkca_mult" parameters, you can create
different amounts of spike frequency adaptation.
Overall, you can see how complex a single compartment model can
be. All the channels are nonlinear systems in themselves, and
when 2-5 channel types are combined, the outcome can be
difficult to predict. In a real neuron, of course, there are
voltage-gated, ligand-gated, and calcium-gated channels
throughout the cell, so a multi-compartment model is necessary to
capture realistic behavior. Interactions, i.e. lateral current
flows, between compartments make a multi-compartment much more
difficult to model realistically.
Each spike that was initiated in the soma back-propagated out
into the dendritic arbor, and if the dendritic arbor was passive,
i.e. it contained no voltage-gated channels, the spike decayed as
it propagated out to the dendritic tips. This charged up the
capacitance of the dendritic arbor, which is typically much
greater than the capacitance of the soma, and the charge then
traveled back to the soma, where it initiated the next spike too
soon. It was a classic case of "impedance mismatch". A passive
dendritic arbor makes the cell spike too fast! By adding Na and
Kdr channels at a slightly lower density than at the soma, spikes
can then back-propagate actively, and the Kdr channels would
discharge the capacitance as the spike propagate out to the
dendritic tips, so it cannot propagate back to the soma. This
arrangement allows the spike generator to fire spikes slowly, as
did the original single comparment model.
Overall, Fohlmeister found that different dendritic morphologies
and their channel densities affect the spike rate generated by
a given input current. It was later verified by Velte & Masland
(1999) that indeed ganglion cells do actively back-propagate
spikes in their dendrites. Although large currents injected into
dendrites can initiate spikes due to the active voltage-gated
channels present, generally the Na channel density is low enough
that typical light-driven synapic inputs don't initiate spikes in
most ganglion cell dendrites. The synaptic currents normally
propagate to the soma and initial segment of the axon to initiate
a spike there, and then actively back-propagate into the
dendrites. The one exception is the direction-selective ganglion
cell (DSGC) that was found to initiate spikes in its dendrites
evoked by light input by Oesch et al (2005).
To see a multi-compartment model of a spike generator, you can go to
nc/models/spikegen and run "nc -v spikegen.n | vid". This model
was developed for the van Rossum, O'Brien & Smith (2003)
paper which investigated the influence of noise properties in
multi-compartment mammalian model. The "spikegen" model also
contains several experiments that can be specified by setting the
"--expt" parameter on the command line.
When noise properties are added, it is even more difficult to
achieve realism -- but noise properties are essential for
understanding the problems that neurons face.
Often when setting up a neural circuit model it is
helpful to remember that a simple model is easier to
understand and possibly more believable than a more
complex one. This is generally true because the
utility of a computational model is often that it
quantitatively assists (stretches) our imagination.
If a model is so complex that we don't understand it,
then it does not help us. If a model uses many
parameters for which numerical values are not known,
then it may be a focus for disbelief.
"Do it in stages"
It is best to first make a simple model to verify
the operation of the model's components. Then enlarge
the model after it gives a threshold of confidence.
For instance, to model a large circuit with many
neurons involved in negative synaptic feedback, it is
best to start with one cell and get its anatomy and
membrane properties worked out. Next set up 2 cells
and their synaptic feedback and verify that the
feedback is working properly using appropriate stimulus
and recording sites.
After the anatomy and basic synaptic model is all
working properly, you should expand the model to
include more cells and complexity. The advantage of
this technique is that any problems that occur can
usually be localized to the addition of a few neural
circuit elements, because everything was developed and
verified in successive stages.
If multiple experiments on a specific model are put into one
model file, this is generally OK if the file isn't too long and
the model is the same for each experiment. But if different
experiments need variations on the construction of the model, it
is best to make a new model file. However, this can cause another
problem, of having too many files, all closely related -- this
can cause confusion and slow development of new models. It is
better to share common parts of multiple related files -- to
reduce the number of files, for clarity and simplicity.
The "spikegen.n" model described above was the precursor for the
"retsim" retinal simulator. It called procedures from several
other files in the "nc" interpreter language -- these gradually
developed into an Applications Programmer Interface (API) that
could construct different neurons and connect them synaptically.
The original "retsim1.n" grew out of this project. The rationale
behind "retsim" is to construct the model with a common set of
algorithms using standard neuron morphologies, biophysical
properties, and synaptic connection types. The experiment file
requests the model to be constructed in this standard manner, and
then need only describe the experimental protocol that is run on
the model, defining stimuli, recording points and plots.
Retsim was next revised using C/C++ as the script language (i.e.
not directly using the nc interpreter) using the original nc API
which is written in C/C++, but revising retsim1.n into retsim.cc.
For retsim.cc, each experiment file is a separate module,
dynamically linked at runtime, and generally contains one
experiment on one specific type of model. This keeps each model
simple and easy to test. Once the model is set up correctly in
the experiment file, then mulitiple experiments can be run on it,
either in the same experiment, or in different but related
experiment files.
arrow keys move around
:wq save and exit.
i insert text
a insert after char
<Esc> stop inserting text
Emacs
Enter text by typing normally. You can move using
the arrow keys. Other "Ctrl" key sequences
allow you to delete and cut and paste.
Mouse button Function
left Set point.
middle Paste text.
right Cut text into X cut buffer.
Shift-middle Cut text into X cut buffer.
Shift-right Paste text.
Ctrl-middle Cut text into X cut buffer and delete it.
Ctrl-right Select window, then split into two.
Running Simulations
neurc file.n Displays graph on screen.
nc -t file.n Displays only numbers on output .
Used for "debugging" a model.
nc file.n > file.r Saves numbers in file.
Used for running long simulations.
nc -v file.n | vid (equivalent to "neurc file.n")
plotmod file.r | vid Displays graph on screen from file.
plotmod file.r | vid -c >file.ps Creates PostScript file
ps2pdf file.ps Creates .pdf file for emailing
How the simulator works
Construction mode
A simple calculation:
print 54/7; // (prints simple calculations)
A print statement within a loop:
for (i=0; i<10; i++)
print i, sqrt(i); // (prints square roots)
Run mode
NeuronC's "run" mode stops "construction" mode and
translates the neural circuit already defined into
difference equations that are numerically integrated at
high speed. During "run" mode, NeuronC numerically
integrates voltage, runs optical and elecrode stimuli,
and plots parameters. Further "construction" must wait
until the run is completed.
statement 1; (these statements construct neural circuit)
statement 2;
statement 3;
.
.
.
step .05; (stops circuit construction, runs 50 msec)
Nodes, neural elements
NeuronC describes circuits as a set of neural
elements ("cable, "sphere", "synapse", etc.) connected
to each other at nodes. A node is a common point at
which neural elements connect electrically to each
other. A node is not a neural element; it only defines
connections between neural elements.
neural element part of a neuron (see list below)
node point to place neural element, can have (x,y,z) location
Element Nodes Description
cable 2 defines multiple compartments.
sphere 1 defines one compartment.
synapse 2 defines connection between 2 nodes.
gap junc 2 defines resistive connection between 2 nodes.
photorecep 1 light transducer connected to node.
load 1 resistor to ground.
resistor 2 defines resistive conn. between 2 nodes (same as g.j.)
cap 2 series capacitor between 2 nodes.
gndcap 1 capacitor to ground; adds capacitance to node.
batt 2 series battery between 2 nodes.
gndbatt 1 battery to ground.
chan 1 active set of channels in membrane.
For neural elements that have 1 node connection, use
the word "at" followed by the node number:
at 20 sphere dia 5
(at node 20, construct a sphere with diameter 5 microns)
For neural elements that have 2 node connections,
use the word "conn" followed by the first node number,
followed by "to" and the second node number:
conn 20 to 30 cable length 100 dia 2;
(between nodes 20 and 30, connect a cable ...)
Each neural element has a set of parameters which
may be specified when the individual neural element is
declared. If a parameter is not defined when the
neural element is defined, it has a default value
specified by a predefined variable. For instance the
default value of membrane resistivity ("Rm") for
passive dendrites is set by the "drm" variable. This
variable may be set with an assignment statment (e.g.
"drm = 3000") like any other variable.
Predefined variables
These variables are set to the following "reasonable" values,
but you can change them with an assignment statement,
e.g. endexp = 0.1;
name default unit meaning of variable
----------------------------------------------------------------
timinc 1e-4 sec time step for numeric integration (sec)
endexp .05 sec time for end of experiment
ploti .001 sec time step for plot increment (sec)
vk -.08 V potassium battery voltage
vna .04 V sodium battery voltage
vcl -.07 V chloride leakage battery voltage
dcm 1 ufd/cm2 default membrane capacitance
dri 200 ohm cm default axial resistance
drg 5e6 ohm um2 default gap junction resistance
drm 40000 ohm cm2 default membrane resistance ohm cm2
Units
NeuronC assumes certain units for biophysical
parameters, and cannot understand units if you type
them in.
diameters and lengths microns
membrane parameters see units in above table.
time seconds, exception synaptic filters = msec
voltages volts
current amperes
resistance Ohms
conductance Siemens
Constructing neural circuits
NeuronC defines a neural circuit with a sequence of
statements much like any programming language. Each
statement is either 1) a neural element statement, or
2) a standard programming statement (as in "C") which
controls how many neural elements will be created. The
analogy to a programming language is that NeuronC
elements are like the printed output from a program; if
a print statement is included inside a "for" loop, many
printed lines will appear in the output. To create
many neural elements, include their definition in a
"for" loop in NeuronC.
conn 1 to 2 cable length 100 dia 1 rm 5000; // constructs cable
stim node 1 vclamp -.01 start .05 dur .01; // adds stimulus
plot V[1]; // adds plot
plot V[2];
step .1; // runs experiment
This simple NeuronC program builds a cable and
defines a stimulus of a voltage clamp to minus 10 mv,
starting at 50 msec into the experiment and stopping
after 60 msec. The voltage at each end of the cable is
plotted. The plotting stops at 0.1 seconds.
Section 2)
Lesson 1) Synaptic input to neuron.
Background:
Model 1:
(Enter the following lines in the editor:)
(c o d e:) ( c o m m e n t s: )
ploti=1e-4;
pre = 100; /* convenience definition */
at pre loc (0,10) sphere dia 1; /* pre = node for presynaptic term. */
/* make synapse */
conn pre to 1 loc (0,0) synapse expon 5 thresh -.05 maxcond 5e-9 vrev 0;
conn 1 to 2 loc (120,0) cable length 120 dia 1 rm 5000; /* make cable */
stim node pre vclamp -.045 start .005 dur .01; /* voltage clamp */
plot V[1] max 0 min -.07; /* plot the voltage at node 1 */
plot V[pre] max 0 min -.07;
if (disp) {
display center (0,0,0);
display size (250);
display matching [-1][-1][-1];
display node matching [-1][-1][-1] color 7;
exit;
};
endexp = .05; /* x axis length on output plot */
step .05; /* length of simulation in sec. */
% neurc mod1
Notes:
tau, the time constant = Rm * Cm
= 5000 * 1e-6
= 5 msec
Lesson 2) Electrotonic decay of voltage in cable
Definitions:
Rm = membrane resistivity (ohm*cm2)
rm = membrane resistance (ohm*cm)
rm = Rm / 2 * PI * radius
Ri = axial resistivity (ohm*cm)
ri = axial resistance (ohm/cm)
ri = Ri / PI * radius2
lambda = sqrt (rm/ri)
tau = Rm * Cm = rm * cm
( c o d e ) ( c o m m e n t s)
ploti = 1e-4;
drm = 5000; /* default Rm = 5000 Ohm-cm2 */
pre = 100; /* pre-synaptic node = 100 */
at pre loc (0,10) sphere dia 1;
conn pre to 1 loc (0,0) synapse expon 5 thresh -.05 maxcond 5e-9 vrev 0;
/* thresh 50 mv, max con 5e-9 S, etc. */
conn 1 to 2 loc (120,0) cable length 120 dia 1; /* construct cable */
conn 2 to 3 loc (240,0) cable length 120 dia 1;
conn 3 to 4 loc (360,0) cable length 120 dia 1;
conn 4 to 5 loc (480,0) cable length 120 dia 1;
conn 5 to 6 loc (600,0) cable length 120 dia 1;
stim node pre vclamp -.01 start 0 dur .01; /* voltage clamp */
plot V[1] max 0 min -.07; /* max and min define */
plot V[2] max 0 min -.07; /* the Y-axis of graph */
plot V[3] max 0 min -.07;
plot V[4] max 0 min -.07;
plot V[5] max 0 min -.07;
plot V[6] max 0 min -.07;
plot V[pre] max 0 min -.07;
if (disp) {
display center (0,0,0);
display size (1000);
display matching [-1][-1][-1];
exit;
};
endexp = .015; /* defines length of X-axis */
step .015; /* run model for 15 msec */
Run the program mod2t by typing:
% neurc mod2t.n
The model consists of a synapse and 5 cable
segments, each 120 microns long, connected together
between 5 nodes. This makes a continuous cable 600
microns long. It is constructed from 5 segments
to allow recording the voltage at several nodes.
velocity = tau/lambda
Next, run the same model with a "space plot" instead
of a "time plot". The space plot is "mod2s.n":
drm = 5000; /* default rm = 5000 */
pre = 100; /* pre-synaptic node = 100 */
at pre loc (10,0) sphere dia 1;
conn pre to 1 (0,0) synapse expon 5 thresh -.05 maxcond 5e-9 vrev 0;
/* thresh 50 mv, max con 5e-9 S, etc. */
conn 1 to 2 loc (120,0) cable length 120 dia 1; /* construct cable */
conn 2 to 3 loc (240,0) cable length 120 dia 1;
conn 3 to 4 loc (360,0) cable length 120 dia 1;
conn 4 to 5 loc (480,0) cable length 120 dia 1;
conn 5 to 6 loc (600,0) cable length 120 dia 1;
if (disp) {
display center (0,0,0);
display size (1000);
display matching [-1][-1][-1];
exit;
};
stim node pre vclamp -.01 start 0 dur .01;
step .01; /* run model for 10 msec */
graph X max 600 min 0; /* set X-axis scale */
graph Y max 0 min -.07; /* set Y-axis scale */
graph init; /* draw X- and Y-axes */
graph (0, V[1]); /* graph volts vs. distance */
graph (120,V[2]);
graph (240,V[3]);
graph (360,V[4]);
graph (480,V[5]);
graph (600,V[6]);
gpen (7); /* make labels for graph */
gmove (0.02,0.85);
gtext ("Volts");
gmove (0.45,0.01);
gtext ("microns");
Run the program mod2s by typing:
% neurc mod2s.n
Notes for mod2s:
lambda = sqrt (rm/ri) = sqrt ((Rm / Ri) * (dia / 4))
2) In an infinite cable, electric current flows away
from the source of current, attenuated by leakage
through membrane conductances. This produces
exponential decay, which causes the voltage to decrease
by a constant ratio over each segment of cable.
Effect of cable diameter
Next, shrink the cable diameter to diameter 0.1
(micron) instead of 1. To run a different model, you
should copy "mod2s" into a new file and modify the new
file:
% cp mod2s mod2ss
Run the simulation with the smaller diameter, and
compare it with the original:
% neurc mod2ss mod2s
Notes for mod2ss:
Lesson 3) Electrotonic decay in dendrite with spines
Background: Many neurons receive input at "spines"
which are short dendritic branches with extremely fine
necks (about 0.1 micron). These spines restrict the
flow of electric current because they are so narrow.
The function of spines for retinal horizontal cells may
be to shape their spatial responses.
% vi mod3
drm = 5000;
pre = 100; /* convenient node definitions */
spine1 = 10;
spine2 = 20;
numsegs = 4; /* number of segments */
seglen = 60; /* length of segments */
spinelen = 5;
totlen = numsegs * seglen + 2 * spinelen;
at pre sphere dia 1;
conn pre to spine1 synapse expon 5 thresh -.05 maxcond 2e-9;
conn spine1 to 1 cable length spinelen dia 0.1; /* spine at beg. of cable */
/* "for" loop saves typing */
for (i=1; i<=numsegs; i++) /* "for segments 1 to numsegs */
conn i to i+1 cable length seglen dia 1;
conn spine2 to 5 cable length spinelen dia 0.1; /* spine at end of cable */
stim node pre vclamp -.01 start 0 dur .01;
step .01; /* run model for 10 msec */
graph X max totlen min 0; /* commands to scale graph */
graph Y max 0 min -.07;
graph init;
graph pen (12);
graph (0, V[spine1]); /* post-synaptic potential */
for (i=0; i<=numsegs; i++) {
if (i==1) graph pen (2); /* i==1 -> (double equals) */
graph (i*seglen+spinelen, V[i+1]); /* graph volts vs. distance */
};
graph pen (1);
graph (totlen, V[spine2]); /* output signal */
gpen (7); /* labels for graph */
gmove (0.02,0.85);
gtext ("Volts");
gmove (0.45,0.01);
gtext ("microns");
Run the program mod3 by typing:
% neurc mod3.n
The model consists of a synapse connecting to the
first spine that in turn connects to a cable of the
same diameter as in "mod2". In a retinal horizontal
cell, each spine is also a site for the neuron's
output. In this model, the neuron's output is located
at the tip of the second spine.
rm = Rm / 2 * PI * radius
ri = Ri / PI * radius2
When the synaptic input current passes through a
spine to enter a neuron, the loss of current through
the spine's membrane resistance is insignificant
compared to the voltage drop across ri.
Lesson 4) Model of Horizontal cell
Background: The retinal horizontal cell is roughly
circularly symmetric, having 5 to 8 branched dendrites
emanating from a large cell body (soma). Input to
horizontal cells comes from photoreceptor synapses
distributed throughout the dendritic tree, and their
output synapses are also distributed throughout the
dendritic tree. Morphology varies with type of
horizontal cell (dendrite length/diameter/ branching
pattern) but it is likely that all horizontal cells
function in a similar way.
% cp mod3.n mod4.n
Edit the file ("mod4.n"):
% vi mod4.n
(Modify "mod4" in the editor to look like this:)
(Soma added!)
( c o d e ) ( c o m m e n t s )
drm = 5000;
pre = 100; /* convenient node definitions */
spine1 = 10;
spine2 = 20;
numsegs = 4; /* number of segments */
seglen = 60; /* lengths of segments */
spinelen = 5;
totlen = numsegs * seglen + 2 * spinelen;
soma = numsegs+1; /* soma is connected to node 5 */
at pre sphere dia 2;
conn pre to spine1 synapse expon 5 thresh -.05 maxcond 2e-9;
conn spine1 to 1 cable length spinelen dia 0.1;
conn spine2 to numsegs+2 cable length spinelen dia 0.1;
for (i=1; i<=numsegs; i++)
conn i to i+1 cable length seglen dia 1;
conn i to i+1 cable length seglen dia 1;
at soma sphere dia 20;
stim node pre vclamp -0.01 start 0 dur 0.01;
step 0.01; /* run model for 10 msec */
graph X max totlen min 0; /* commands to scale graph */
graph Y max 0 min -.07;
graph init;
graph pen (12);
graph (0, V[spine1]); /* post-synaptic potential */
for (i=0; i<=numsegs; i++) {
if (i==1) graph pen (2);
graph (i*seglen+spinelen, V[i+1]); /* graph volts vs. distance */
};
graph pen (1);
graph (totlen, V[spine2]); /* output signal at spine 2*/
gpen (7); /* labels for graph */
gmove (0.02,0.85);
gtext ("Volts");
gmove (0.45,0.01);
gtext ("microns");
Run the program mod4 by typing:
% neurc mod4
Run the simulation:
% neurc mod4
Notes for mod4:
neurc mod4 mod4a
neurc mod4 mod4a mod4b
Note that the effect of placing the soma halfway
along the main dendrite is to reduce the length of the
dendrite and slightly increase signal at the soma. The
signal arriving at spine 2 is only slightly reduced by
traversing the distal part of the main dendrite
(between soma and spine 2).
neurc -d 1 mod4d.n
To see a display of the node numbers, you can run mod4d.n like
this:
neurc -d 9 mod4d.n
Lesson 5) Model of photoreceptor network
Background: Photoreceptors in all vertebrates are
coupled by gap junctions, which spread electrical
signals laterally. Gap junctions therefore couple
photoreceptors into a large 2-dimensional syncytium
(coupled neural array). In effect, this coupling
"blurs" visual signals after they are transduced by
photoreceptor outer segments. This blur is an
essential part of retinal signal processing. Its
function is to filter out spatial high-frequency
signals before they traverse the first chemical
synapse.
% vi mod5t.n
Enter the following lines:
(c o d e) /* c o m m e n t s */
endexp = .15; /* x axis length for plot */
drm = 5000;
for (row=0; row<35; row+=5) /* create cone array */
for (col=0; col<35; col+=5) { /* nested "for" loops */
at [row][col] cone (row,col) maxcond 1e-9;
at [row][col] sphere dia 10;
};
drg = 1; /* calibration for gsiz in Siemens */
gsiz = 1e-8; /* 1 connexon = 100 pS */
for (row=0; row<30; row+=5) /* connect gj's between rows */
for (col=0; col<35; col+=5) {
conn [row][col] to [row+5][col] gj gsiz;
};
for (row=0; row<35; row+=5) /* connect gj's between columns*/
for (col=0; col<30; col+=5) {
conn [row][col] to [row][col+5] gj gsiz;
};
cent = 15;
stim spot 1 loc (cent,cent) inten 1e7 start .01 dur 1e-3;
/* spot 1 um diam; inten 1e7 phot/um2/sec; dur 1 msec */
plot V[0][0] max -.031 min -.035; /* plot corner response */
for (dist=0; dist<35; dist+= 5) { /* plot line though center */
plot V[cent][dist] max -.031 min -.035;
};
plot L[cent][cent] max 5e7 min 0; /* plot light flash */
step .15;
Run the simulation:
% neurc mod5t
Notes:
1) Note that mod5t gives a plot of the cones'
response voltage versus time. The cones take about 10
msec. to initially reach an equilibrium potential.
Compare the response of the central cone with the
others in the array. The central cone's response is
considerably reduced because of lateral current flow
through the gap junctions.
drm = 5000;
for (row=0; row<35; row+=5) /* create cone array */
for (col=0; col<35; col+=5) {
at [row][col] cone (row,col) maxcond 1e-9;
at [row][col] sphere dia 10;
};
drg = 1; /* calibration for gsiz in Siemens */
gsiz = 1e-8;
for (row=0; row<30; row+=5) /* connect gj's between rows */
for (col=0; col<35; col+=5) {
conn [row][col] to [row+5][col] gj gsiz;
};
for (row=0; row<35; row+=5) /* connect gj's between columns*/
for (col=0; col<30; col+=5) {
conn [row][col] to [row][col+5] gj gsiz;
};
cent = 15;
stim spot 1 loc (cent,cent) inten 1e7 start .01 dur 1e-3;
step .07;
graph X max 30 min 0; /* commands to scale graph */
graph Y max -.031 min -.035;
graph init;
graph pen (12);
graph (0, V[0][0]); /* corner cone */
for (dist=0; dist<35; dist += 5) { /* plot line though center */
graph (dist, V[cent][dist]); /* graph volts vs. distance */
};
gpen (7); /* labels for graph */
gmove (0.02,0.85);
gtext ("Volts");
gmove (0.45,0.01);
gtext ("microns");
Remember that mod5s takes about 30 seconds to run.
Be patient while the cone responses are recorded at
their maximum.
row = 100;
col = 100;
cent = 10;
at [row][col] cone (cent,cent); /* make single isolated cone */
at [row][col] sphere dia 5;
plot V[row][col] max -.02 min -.07; /* plot the isolated cone */
But perhaps an easier way to look at "isolated"
cones in this type of model is to stimulate all of them
with a spot large enough to "cover" all of them. Try
increasing the size of the spot to 100 microns. In
this case, there is no lateral coupling because each
cone has an identical response. This approach requires
more computation, though!
Lesson 6) Model of wide-field amacrine cell.
Background: Many amacrine cells have a distinctive
morphology consisting of extremely long, fine dendritic
processes emanating from the soma. The dendritic
processes enlarge to form small beads or "varicosities"
every 5 to 10 um. Each varicosity typically contains
one input and one output synapse. It is likely that
the space constant of the fine dendritic processes is
relatively short (i.e. less than 50 um); therefore the
function of this type of amacrine cell is probably
local processing.
% vi mod6t.n
Enter the following lines:
/* amacrine dendrite with varicosities */
/* temporal plot */
drm = 5000;
endexp = 0.02;
nsegs = 10;
seglen = 10;
totlen = seglen * nsegs;
varicos = 4;
synap = 100;
for (i=1; i<=nsegs; i++) {
at [i][synap] sphere dia 3; /* presynaptic terminal */
conn [i][synap] to [i] synapse expon 5 maxcond 5e-9 thresh -0.04 vrev -0.01;
at i sphere dia varicos; /* the varicosity */
conn i to i+1 cable length seglen dia 0.1; /* the fine cable */
if (i==5) stim node [i][synap] vclamp -.025 start 0 dur 0.01
/*else stim node [i][synap] vclamp -.030 start 0 dur 0.05; */
};
at i sphere dia 5;
for (i=1; i<=nsegs; i++) {
plot V[i] max -0.01 min -0.07;
};
step .02;
Now, exit the editor. Run the simulation:
% neurc mod6t
Notes
/* amacrine dendrite with varicosities */
/* spatial plot */
drm = 5000;
nsegs = 10;
seglen = 10;
totlen = seglen * nsegs;
varicos = 4;
synap = 100;
for (i=1; i<=nsegs; i++) {
at [i][synap] sphere dia 3; /* presynaptic terminal */
conn [i][synap] to [i] synapse expon 5 maxcond 5e-9 thresh -.04 vrev -.01;
at i sphere dia varicos; /* the varicosity */
conn i to i+1 cable length seglen dia 0.1; /* the fine cable */
if (i==5) stim node [i][synap] vclamp -0.025 start 0 dur 0.01;
/* else stim node [i][synap] vclamp -0.030 start 0 dur 0.05; */
};
at i sphere dia 5;
graph X max totlen min 0;
graph Y max -0.01 min -0.07;
graph init;
gpen (7); /* labels for graph */
gmove (0.02,0.85);
gtext ("Volts");
gmove (0.45,0.01);
gtext ("microns");
stim node [seglen][synap] vclamp -.045 start 0.01 dur 0.02;
graph pen (2);
stepsiz=0.001;
for (t=0; t<0.02; t+=stepsiz) {
step stepsiz;
graph restart;
if (t>=.01) graph pen (4);
if (t==0.01) stim node [i][synap] vclamp -0.045 start 0.01 dur 0.02;
for (i=0; i<=nsegs; i++) {
graph (i*seglen, V[i+1]); /* graph volts vs. distance */
};
};
Now, exit the editor. Run the simulation:
% neurc mod6s
Notes:
if (i==5) stim node [i][synap] vclamp -.025 start 0 dur .01
else stim node [i][synap] vclamp -.030 start 0 dur .05;
Also, modify the Y min value for the graph:
graph Y max -.01 min -.04;
Then run the model:
neurc mod6s
Notes:
Section 3)
To learn about spiking neurons, you can run the "scomp" series
of models in nc/tcomp. They are single-compartment models with
several membrane channels that together form a spike generator.
scomp_fm.n single compartment model based on Fohlmeister & Miller (1997a)
scomp_fm2.n single compartmen model based on Fohlmeister & Miller (1997a), modified
scomp_a.n shows spike adaptation.
scomp_b.n similar to scompa.n, tuned to 37 deg
scomp_c.n derived from scompa.n @ 22 deg C subst "ndensity" for "density"
scomp_d.n similar to scompc.n, tuned to 37 deg
scomp_persis.n sets up persistent Na current, controlled by ifactor
scomp_ad*.n series of models tuned to 37 deg, used to develop Mark van Rossum's (2003) model
scomp_ad6.n contains several experiments, many params, can be run at diff temperatures
Scomp models: single compartment spike generator
The Fohmmeister & Miller (1997) model
at soma sphere dia 25 vrest grest vrev -.06;
This specified a cell with 25 um diameter soma, with Rm = 50000
(set above by drm=50000), and a battery voltage for Rm of -60 mV.
The spike experiment
neurc scomp_fm.n | vid
or
neurc --expt spike scomp_fm.n | vid
This experiment is:
if (expt=="spike") { /* look at spike shape */
stim node soma cclamp 250e-12 start 0 dur .0005;
stim node soma cclamp 150e-12 start .0005 dur .0015;
endexp = .006;
plgain = 5e-9;
naoff = 0;
nagain = plgain;
caoff = 0;
cagain = plgain;
kdroff = 0;
kdrgain = plgain;
kaoff = 0;
kagain = plgain;
skoff = 0;
skgain = plgain;
bkoff = 0;
bkgain = plgain;
plot G(I) naxx pen 1 max (naoff+1) * nagain min (naoff-1) * nagain; // blue trace
plot G(I) kdr pen 2 max (kdroff+1)* kdrgain min (kdroff-1)* kdrgain; // green trace
plot G(I) ka pen 14 max (kaoff+1) * kagain min (kaoff-1) * kagain; // yellow trace
plot G(I) ca1 pen 3 max (caoff+1) * cagain min (caoff-1) * cagain; // cyan trace
if (!notinit(skca1))
plot G(I) skca1 pen 5 max (skoff+1)*skgain min (skoff-1) * skgain; // magenta trace
if (!notinit(skca2))
plot G(I) skca2 pen 8 max (skoff+1)*skgain min (skoff-1) * skgain; // gray trace (if uncommented)
if (!notinit(bkca))
plot G(I) bkca pen 7 max (bkoff+1)*bkgain min (bkoff-1) * bkgain; // white trace (if uncommented)
plot V[soma] pen 4 max .16 min -.08; // red trace
plot S totcur pen 12 max plgain min -plgain; /* total current from onplot(), dark red trace */
}
plot G(I) naxx pen 1 max (naoff+1) * nagain min (naoff-1) * nagain; // blue trace
The "naoff" and "nagain" variables in the plot statement are
suppoed to allow the user to offset the traces and change the
relative scaling, to make the overlapping traces easier to see.
For example, the Na current is much larger initially than the
other currents, so sometimes it is helpful to increase nagain
which then gives a smaller scaling to the Na current, allowing
the complete waveshape to be easily seen. For most purposes,
though, one wants to see all the currents at the same scale, so
all the gains are set to the same value: +/- 5e-9.
The inter-spike interval
In some spike generators that have only Na, Kdr, and KA channels,
the KA current plays a special role in which it activates a
little, soon after the refractory period, at a relatively
hyperpolarized voltage. This slows the ramping up depolarization
to the next spike, which may be important for some spike
generators that require large currents to start spiking. By
slowing the ramping depolarization, this allows the spike
generator to initiate spikes farther apart in time (longer
inter-spike interval), i.e. to make a slower spike train. But
then KA will inactivate, depending on how much depolarization it
sees, also at a relatively hyperpolarized voltage, which then
allows faster ramping depolarization, and a spike to occur more
immediately when the Na channel gets activated.
neurc --expt isi scomp_fm.n | vid
else if (expt=="isi") { /* look at inter-spike interval */
waittime = 0.0004;
stimdur = 1;
afterstim = 0.10;
stimampl = 45e-12;
stim node soma cclamp 200e-12 start 0 dur waittime;
stim node soma cclamp stimampl start waittime dur stimdur;
endexp = .025;
//endexp = .5;
plgain = 2e-10;
naoff = 0;
nagain = plgain;
caoff = 0;
cagain = plgain;
kdroff = 0;
kdrgain = plgain;
kaoff = 0;
kagain = plgain;
kacgain = plgain*10;
skoff = 0;
skgain = plgain;
bkoff = 0;
bkgain = plgain;
moff = 1;
mgain = plgain;
plot G(I) naxx pen 1 max (naoff+1) * nagain min (naoff-1) * nagain;
plot G(I) kdr pen 2 max (kdroff+1)* kdrgain min (kdroff-1)* kdrgain;
plot G(I) ka pen 14 max (kaoff+1) * kagain min (kaoff-1) * kagain;
//plot G(0) ka pen 2 max (kaoff+1) * kacgain min (kaoff-1) * kacgain;
plot G(I) ca1 pen 3 max (caoff+1) * cagain min (caoff-1) * cagain;
if (!notinit(skca1))
plot G(I) skca1 pen 5 max (skoff+1)*skgain min (skoff-1) * skgain;
if (!notinit(skca2))
plot G(I) skca2 pen 8 max (skoff+1)*skgain min (skoff-1) * skgain;
if (!notinit(bkca))
plot G(I) bkca pen 7 max (bkoff+1)*bkgain min (bkoff-1) * bkgain;
plot V [soma] pen 4 max .16 min -.08;
plot Im[soma] pen 12 max (moff+1)*mgain min (moff-1) * mgain;
plot Ca(1)[soma] pen 6 max 20e-6 min 0; /* [Ca]i */
}
Role of currents in inter-spike interval
neurc --expt f/i --bkca_mult 0 --skca2_mult 1 scomp_fm.n | vid
To see the influence of the random gating of the channels, run
the model with "channoise 1" on the command line:
neurc --expt isi --bkca_mult 0 --skca2_mult 1 --channoise 1 scomp_fm.n | vid
This gives some intuition about what the noise that typical
neurons have to deal with. The greater density of channels, the
less the noise problemm becomes.
Other scomp models
The other scomp models are built upon scomp_fm.n, but are
designed to describe a mammalian cell, which lives at warmer
temperatures than a salamander. Their "tempcel" (temperature of
the cell in Celsius) is set to 35 degrees which greatly increases
the kinetic rate of the activation and inactivation of the
channel currents. The Na current rises much faster, and the
depolarization of the spike rises much faster, typically in 0.1 -
0.2 msec. In this case, the capacitance of the cell is much more
of a factor, i.e. since the rise time is much faster, for the
same capacitance (set by the cell dimensions) the voltage-gated
currents must be much larger, typically 3-fold greater (140e-3
vs.50e-3 S/cm2). In scomp[a-e].n the channel densities are set
using "ndensity" which is the number of channels per um2. This is
calculated from the standard for channel densities, S/cm2, by
dividing by the unitary channel current amplitude, given by
qcond(unitarycurr), where qcond() is adjusts the unitary current
from cm2 to um2 also by the model temperature. In the
"scomp_ad?.n" models, the ndensity values are given as n/um2
which is equivalent to the other way of specifying, either using
qcond() or using "density". This is supposed to help the user get
more intuition about the actual density of channels in a typical
cell.
Scomp summary
Try modifying any of these models, by changing the channel
densities and looking at the different experiments. See if you
can understand how the currents develop at the beginning of the
spike, how the spike ends, and how the spike interval is
controlled. You can do this by adding parameter values on the
command line.
Multi compartment spiking neuron
The second paper in the Fohlmeister & Miller (1997b) series
shows how adding a dendritic arbor to a neuron greatly affects
how the spike generator works. Before this classic paper, it was
thought that ganglion cell dendrites were essentially passive
collectors of the synaptic currents that define the spike rate.
However, Fohlmeister discovered that adding a dendritic arbor to
a single compartment spike generator that had been already
calibrated caused the spike generator to fail.
Section 4)
Design philosophy
Design philosophy: "keep it simple!"
Retsim
Copyright (C) 2024
Robert G. Smith
Department of Neuroscience
Univ. of PA Medical School
Phila., PA 19104-6058
USA
All Rights Reserved